Lesson: Assumptions in Geometry

Comment on Assumptions in Geometry

At 3:18, it is told that angle ABC refers to the smaller angle. However, it is also mentioned in this video itself that no assumptions should be made about angle measurements. Aren't these 2 assumptions contradictory?
greenlight-admin's picture

I don't think they're contradictory.

Making no assumptions about angle measurements means we can't look at an angle and say "That angle looks like 90 degrees, or 45 degrees, etc"

The part about ∠ABC referring to the smaller angle is a general construct we use for angle notation. It doesn't have anything to do with assuming the value (in degrees) of a given angle.

I hope that helps.

Cheers,
Brent

greenlight-admin's picture

While deleting some spam posts today, I accidentally deleted a legitimate question (below). However, I don't know who the author was.

1:11 - Both lines appear to be perfectly straight. It is right to assume straight looking lines are indeed straight, and thus have a 180 degree angle each. Because these 2 straight lines intersect, and because we have correctly assumed they have perfect 180 degree angles, we can assume they are perpendicular, and thus when they intersect they form 90 degree angles. Yet, we cannot assume x is 90 degrees. I find this contradictory.

As you might imagine, it would be difficult to label every straight line as 180 degrees. I believe this is the test-maker's rationale. Alternatively, if we don't label right angles as such, then we could assume most angles are 90 degrees.

I hope that helps.

Cheers,
Brent

https://greprepclub.com/forum/s-is-the-midpoint-of-segment-pr-9563.html

For this problem given the fact that the image is not drawn to scale. Can't we swing line QT along the triangle PQR therefore making QT equal to QR and even making it extremely small as well?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/s-is-the-midpoint-of-segment-pr-9563.html

Although the diagram is not drawn to scale, there are a few facts that we still need to adhere to.
For example, the diagram indicates that point T lies BETWEEN points P and S, which means side QT must be shorter than side QP.

From here, we can use the fact that, since QS is a perpendicular bisector, we can conclude that triangle PQR is an isosceles triangle in which PQ = QR.
So, if side QT is shorter than side QP, then it must also be true that side QT is shorter than side QR.

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